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NON-NEGOTIBLE EVALUATION CRITERIA
2018-2024
Group VI – Mathematics
Grade 4
Equity, Accessibility and FormatYes / No / N/A / CRITERIA / NOTES
1. INTER-ETHNIC
The instructional materials meets the requirements of inter-ethnic: concepts, content and illustrations, as set by WV Board of Education Policy (Adopted December 1970).
2. EQUAL OPPORTUNITY
The instructional material meets the requirements of equal opportunity: concepts, content, illustration, heritage, roles contributions, experiences and achievements of males and females in American and other cultures, as set by WV Board of Education Policy (Adopted May 1975).
3. FORMAT
This resource is available as an option for adoption in an interactive electronic format.
4. BIAS
The instructional material is free of political bias.
GENERAL EVALUATION CRITERIA
2018-2024
Group VI – Mathematics
Grade 4
The general evaluation criteria apply to each grade level and are to be evaluated for each grade level unless otherwise specified. These criteria consist of information critical to the development of all grade levels. In reading the general evaluation criteria and subsequent specific grade level criteria, e.g. means “examples of” and i.e. means that “each of” those items must be addressed. Eighty percent of the general and eighty percent of the specific criteria must be met with I (in-depth) or A (adequate) in order to be recommended.
(Vendor/Publisher)SPECIFIC LOCATION OF CONTENT WITHIN PRODUCTS / (IMR Committee) Responses
I=In-depth, A=Adequate, M=Minimal, N=Nonexistent / I / A / M / N
In addition to alignment of Content Standards, materials must also clearly connect to Learning for the 21st Century which includes opportunities for students to develop:
Use Problem Solving Skills
For student mastery of content standards, the instructional materials will include multiple strategies that provide students with opportunities to:
1. Make sense of problems and persevere in solving them;
2. attend to precision;
3. deepen understanding through meaningful and challenging teacher and/or student directed inquiry-based learning that builds number sense using prior knowledge and promotes interdisciplinary connections;
4. reason abstractly and quantitatively;
5. construct viable arguments and critique the reasoning of others
6. make informed choices by interacting with outside resources through opportunities for local and global collaboration in a variety of safe venues
7. model with mathematics;
8. use appropriate tools strategically;
9. use appropriate technology tools for a variety of purposes
10. look for and make use of structure
11. look for and express regularity in repeated reasoning.
Personal and Workplace Productivity Skills
For student mastery of content standards, the instructional materials will include multiple strategies that provide students with opportunities to:
12. work collaboratively;
13. practice time-management and project management skills in problem-based learning situations.
Developmentally Appropriate Instructional Resources and Strategies
For student mastery of content standards, the instructional materials:
14. are designed to devote the large majority of time to the critical areas of the grade as noted in the narrative written above the grade level standards;
15. include suggestions for appropriate scaffolding and provide opportunities to engage in high interest, age‐appropriate activities that simulate real‐life situations, and make cross‐curricular, global connections;
16. provide students with opportunities to use print, graphs, visual displays, developmentally appropriate manipulatives, media and technology sources to acquire and apply new information;
17. include best practices that emphasize the importance of authentic vocabulary acquisition using multiple methods and modes that motivate and increase vocabulary skills;
18. support personalized learning through intervention and enrichment activities;
19. provide a dynamic, interactive website for students to access electronic resources (i.e., podcasts, videos, skill-based games, etc.). The media included in the instructional materials must enhance and support instruction and learning;
20. include a professional resource that builds content and pedagogical knowledge for the teacher.
Assessment
21. Instructional materials provide tools for a balanced approach to assessment including diagnostic, formative and summative assessments in multiple formats (i.e., rubrics, performance tasks, open-ended questions, portfolio evaluation, and multimedia simulations).
Organization, Presentation and Format
22. Information is organized logically and presented clearly using multiple methods and modes for delivering differentiated instruction that motivates and increases numeracy as students engage in high interest, authentic activities.
23. Instructional materials include an electronic file of the student edition provided on an electronic data storage device (e.g., CD, DVD, USB drive, etc.) and through a link on the publisher’s server, both of which are accessible by an internet-enabled device that can open standard file formats.
24. The materials engage parents in appropriate ways. For example, homework assignments in elementary grades consists of routine problems, practice with getting answers and fluency-building exercises that parents can easily support.
SPECIFIC EVALUATION CRITERIA
2018-2024
Group VI – Mathematics
Grade 4
All West Virginia teachers are responsible for classroom instruction that integrates content standards and mathematical habits of mind. Students in the fourth grade will focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. Mathematical habits of mind, which should be integrated in these content areas, include: making sense of problems and persevering in solving them, reasoning abstractly and quantitatively; constructing viable arguments and critiquing the reasoning of others; modeling with mathematics; using appropriate tools strategically; attending to precision, looking for and making use of structure; and looking for and expressing regularity in repeated reasoning. Continuing the skill progressions from third grade, the following chart represents the mathematical understandings that will be developed in fourth grade:
Operations and Algebraic Thinking / Number and Operations in Base Ten· Use whole-number arithmetic to solve word problems, including problems with remainders and problems with measurements.
· Add and subtract whole numbers quickly and accurately (numbers up to 1 million).
· Multiply and divide multi-digit numbers in simple cases (e.g., multiplying 1,638 × 7 or 24 × 17, and dividing 6,966 by 6).
· Gain familiarity with factors and multiples.
· Generate and analyze patterns. / · Generalize place value understanding for multi-digit whole numbers.
· Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations- Fractions / Measurement and Data
· Use equivalent fractions to understand and order fractions (e.g., recognize that 1⁄4 is less than 3⁄8 because 2⁄8 is less than 3⁄8).
· Add, subtract, and multiply fractions in simple cases (such as 2 3⁄4 − 1 1⁄4 or 3 × 5⁄8), and solve related word problems.
· Understand and compare simple decimals in terms of fractions (e.g., rewriting 0.62 as 62⁄100). / · Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
· Represent and interpret data.
· Geometric measurement: understand concepts of angle and measure angles.
Geometry
· Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
· Measure angles and find unknown angles in a diagram.
For student mastery of content standards, the instructional materials will provide students with the opportunity to
(Vendor/Publisher)SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCTS / (IMR Committee) Responses
I=In-depth, A=Adequate, M=Minimal, N=Nonexistent / I / A / M / N
Operations and Algebraic Thinking
Use the four operations with whole numbers to solve problems.
1. Interpret a multiplication equation as a comparison (e.g., interpret 35 =
5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations.
2. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison.
3. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Gain familiarity with factors and multiples.
4. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
Generate and analyze patterns.
5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.)
Number and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
6. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division).
7. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.
8. Use place value understanding to round multi-digit whole numbers to any place.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
9. Fluently add and subtract multi-digit whole numbers using the standard algorithm.
10. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models.
11. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models.
Number and Operations - Fractions
Extend understanding of fraction equivalence and ordering.
12. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
13. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
14. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8).
c. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem.
15. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b).
c. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?).
Understand decimal notation for fractions and compare decimal fractions.
16. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.
17. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram).
18. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model.